I'm worried about the first of the month falling on a Friday such as tomorrow, April 1st. Will the weekend squash the popularity of a Friday 'Who's Hiring' thread?
I don't think that has much to do with using a separate, automated account to make the posts.
If weekends turn out to be an issue, the person running the posting script can just edit the post date (e.g. set it to "the first monday of the month") or whatever.